Towards extracellular Ca 2+ sensing by MRI: synthesis and calciumdependent. ligands

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1 Towards extracellular Ca 2+ sensing by MRI: synthesis and calciumdependent 1 H and 17 O relaxation studies of two novel bismacrocyclic ligands Kirti Dhingra, a Petra Fousková, b Goran ngelovski, a Martin E. Maier, c Nikos K. Logothetis, a,d Éva Tóth* b a Max Planck Institute for Biological Cybernetics, Tübingen, Germany b Centre de Biophysique Moléculaire, CNRS, Orléans Cedex 2, France c Institute für Organische Chemie, Universität Tübingen, Germany d Imaging Science and Biomedical Engineering, University of Manchester, Manchester, U.K. ppendix. Equations used in the analysis of 17 O NMR and 1 H NMRD data. Table S1. Proton relaxivities (r 1 / mm -1 s -1 ) of Gd 2 L 1 in the absence of Ca 2+, c(gd 3+ )=5.1 mm, ph=6.25, at 25 and 37 C. Table S2. Proton relaxivities (r 1 / mm -1 s -1 ) of Gd 2 L 1 in the presence of Ca 2+, c(gd 3+ )=3.2 mm, c(ca 2+ )=4.4 mm, ph=7, at 15.5, 25 and 37 C. Table S3. Variable temperature reduced transverse and longitudinal 17 O relaxation rates of Gd 2 L 1 in the absence of Ca 2+, c(gd 3+ )=51.8 mm, ph=7, P m = at T. Reference was acidified H 2 O, ph=3.4. Table S4. Variable temperature reduced transverse and longitudinal 17 O relaxation rates of Gd 2 L 1 in the presence of 1M Ca 2+, c(gd 3+ )=45.6 mm, ph=7, P m = at T. Reference was acidified 1M CaCl 2. Table S5. Relaxometric Ca 2+ titration of Gd 2 L 1 at 25 C, ph neutral and T. Table S6. Relaxometric Ca 2+ titration of Gd 2 L 2 at 25 C, ph neutral and T. Table S7. Relaxometric Mg 2+ titration of Gd 2 L 1 at 25 C, ph neutral and T. Table S8. Luminescence lifetimes measurements on Eu 2 L 1 at 25 C, ph neutral, and the calculated hydration numbers q. Figure S1. Variable Ca 2+ concentration UV-Vis studies on Eu 2 L 1 at 50 C. Figure S2. Variable Ca 2+ concentration UV-Vis studies on Eu 2 L 1 at 37 C. Figure S3. Variable Ca 2+ concentration UV-Vis studies on Eu 2 L 1 at 25 C. Figure S4. Variable Ca 2+ concentration UV-Vis studies on Eu 2 L 1 at 15.5 C. Table S9. Fitted parameters of Gd 2 L 1 in the absence of Ca 2+. The underlined parameters were fixed during the fitting. Table S10. Fitted parameters of Gd 2 L 1 in the presence of 1M Ca 2+. The underlined parameters were fixed during the fitting. Figure S5. IR spectrum of the ligand L 1. Figure S6. IR spectrum of Gd 2 L 1 complex. Figure S7. 1 H NMR spectrum of the compound 6a. Figure S8. 13 C NMR spectrum of the compound 6a. Figure S9. 1 H NMR spectrum of the ligand L 1. Figure S C NMR spectrum of the ligand L 1. Figure S11. 1 H NMR spectrum of the ligand L 2. Figure S C NMR spectrum of the ligand L 2. Figure S13. 1 H- 1 H COSY spectrum of the compound 6a. Figure S14. 1 H- 13 C HSQC spectrum of the compound 6a.

2 Equations. 17 O NMR relaxation: From the measured 17 O NMR relaxation rates of the paramagnetic solutions, 1/T 1 and 1/T 2, and of the acidified water reference, 1/T 1 and 1/T 2, one can calculate the reduced relaxation rates, 1/T 1r, 1/T 2r (Eq. [1] and [2]), where 1/T 1m, 1/T 2m are the relaxation rates of the bound water and Δω m is the chemical shift difference between bound and bulk water, τ m is the mean residence time or the inverse of the water exchange rate k ex and P m is the mole fraction of the bound water. 1, = T1r P m T1 T = + [1] 1 T1m + τ m T1 OS T2m + τmt2m +Δωm 1 = T 2 2r P m T2 T = + [2] 2 τ m τ + T +Δω T2OS ( 2 ) m m m The terms 1/T 1OS and 1/T 2OS describe relaxation contributions from water molecules not directly bound to the paramagnetic centre. In previous studies it has been shown that 17 O outer sphere relaxation terms due to water molecules freely diffusing on the surface of Gd-polyaminocarboxylate complexes are negligible. For complexes with electronegative groups relaxation terms due to 2 nd sphere water molecules can however be important for longitudinal relaxation 1/T 1r and have therefore to be included = + = + [3] 1st 2nd 2nd T1r T1r T1r T1 m + τ m T1r T2m + τ m T2m +Δωm = = [4] 1st T 2 2r T2r τ m τ + T +Δω ( 2 ) m m m First sphere contribution to 17 O relaxation: The 17 O longitudinal relaxation rates in Gd(III) solutions are the sum of the contributions of the dipole-dipole and quadrupolar (in the approximation developed by Halle for non-extreme narrowing conditions) mechanisms as expressed by Eq. [6]-[7], where γ S is the electron and γ I is the nuclear gyromagnetic ratio (γ S = rad s -1 T -1, γ I = rad s -1 T -1 ), r GdO is the effective distance between the electron charge and the 17 O nucleus, I is the nuclear spin (5/2 for 17 O), χ is the quadrupolar coupling constant and η is an asymmetry parameter: = + [5] T T T 1m 1dd 1q μ 0 h I S = γ γ S 6 ( S 1) 3 J ( ωi; τd1) 7 J ( ωs; τd2) ; J ( ω; τ) τ 2 1dd 15 4π + + = r GdO 1 + T ( ωτ ) τ = d1 τ + m T + 1e τro π 2I η = χ J 2 ( ωi; τro) J ( ωi; τro) ; Jn ( ω; τ) = τ T1 q 10 I ( 2I 1) nωτ ( ) In the transverse relaxation the scalar contribution, 1/T 2sc, is dominating, Eq. [8]. 1/τ s1 is the sum of the exchange rate constant and the electron spin relaxation rate S( S + 1) = τ [8] S1 T2m T2SC 3 h = + [9] τ τ T S1 m 1e Second sphere contribution to 17 O relaxation: [6] [7]

3 2nd 2nd 1 q 1 q 1 1 = 2nd 1st 2nd 1st + 2nd 2nd T1 q T1m q T1dd T 1q 1 3τ =C + 2nd,O 2nd,O 2nd,O d1 d2 2nd dd 2 2 T1dd 1+ ωτ 1+ ωτ 7τ 2nd,O 2nd,O ( I d1 ) ( S d2 ) nd,O 2 μ 17 0 h γ γ O S C dd = S S+1 2nd π r ( GdO ) ( ) 1 3π 2I τ 0.8τ ( ) T I 2I 1 1+ ωτ 1+ 2ωτ 2 2nd,O 2nd,O 2 2 = χ 1+η 3 + 2nd q 10 ( ) = + τ τ τ τ O,2nd O O g l l τ 2nd =k 2nd,O ex + + O,2nd di τ T ie 2nd,O 2nd,O ( I ) ( I ) [10] [11] [12] [13] [14] 1 H NMRD: obs The measured longitudinal proton relaxation rate, R 1 is the sum of a paramagnetic and a diamagnetic contribution as expressed in Eq. [15], where r 1 is the proton relaxivity: obs d p d 3 R1 = R1 + R1 = R1 + r1 Gd + [15] The relaxivity is here given by the sum of inner sphere, second sphere and outer sphere contributions: r = r + r + r [16] 1 1is 1,2nd 1os Inner sphere 1 H relaxation: The inner sphere term is given in Eq. [17], where q 1st is the number of inner sphere water molecules. 3 1st 1 q 1 r1 is = [17] H T1 m + τ m The longitudinal relaxation rate of inner sphere protons, 1/T H 1m is expressed by Eq. [18], where r GdH is the effective distance between the electron charge and the 1 H nucleus, ω I is the proton resonance frequency and ω S is the Larmor frequency of the Gd(III) electron spin μ0 h γ Iγ S = 6 ( 1) 3 ( I; d1) 7 ( S; H S S + J ω τ + J ω τd2) T1 m 15 4π r [18] GdH 2 2 S τ ( 1 S ) τ dig di J ( ωτ ; di ) = + ; i = 1,2 [19] ωτdig 1+ ωτ di = + + ; H τ τ τ T τ = τ + τ + T ; i = 1,2 [20] dig m g ie = + H H τ τg τl dig m ie The spectral density functions are given by Eq. [19]. Second sphere 1 H relaxation: [21]

4 2nd 2nd 2nd 1 q 1 1 q 1 1 T 2nd,H 2nd,H 1dd + τ 2nd m T 1dd r = τ 2nd,H 2nd,H 2nd,O d1 d2 =C 2nd,H dd T1dd 1+ ωτ 1+ ωτ 7τ 2nd,H 2nd,H ( I d1 ) ( S d2 ) nd,H 2 μ 1 0 h γ γ H S C dd = S S+1 2nd π r ( GdO ) =k + + 2nd 2nd,H ex H τdi τ Tie = + H H τ τg τl ( ) [22] [23] [24] [25] [26] Outer sphere 1 H relaxation: The outer-sphere contribution can be described by Eq. [27] where N is the vogadro constant, and J os is its associated spectral density function. 4, N π μ0 h γ Sγ I 1os = + os I 1e + os S 2e 405 4π agdh DGdH ( 1) 3 ( ω ; ) 7 ( ω ; ) r S S J T J T 1/2 1 τ GdH 1+ iωτgdh + 4 Tje Jos ( ω, Tje ) = Re ; j = 1,2 [28] 1/2 3/2 τ GdH 4 τ GdH 1 τ GdH 1+ iωτgdh + + iωτgdh + + iωτgdh + T je 9 T je 9 T je 2 agdh τ GdH = [29] DGdH a GdH is the distance of closes approach and D GdH is the diffusion coefficient for the diffusion of a water proton relative to the Gd(III) complex. Electron spin relaxation: The longitudinal and transverse electronic relaxation rates, 1/T 1e and 1/T 2e are described by Solomon- Bloembergen-Morgan theory modified by Powell (Eqs. [30]-[31]), where τ V is the correlation time for the modulation of the zero-field-splitting interaction. ZFS = Δ τ v { 4S( S + 1) 3} [30] T1 e ωsτv 1+ 4ωSτv ZFS =Δ τ v [31] T2 e ωSτv ωSτv [27] Temperature dependences of water exchange rates and correlation times: The exchange rates are supposed to follow the Eyring equation. In Eq. [32] ΔS and ΔH are the entropy and enthalpy of activation for the water exchange process, and k ex 298 is the exchange rate at K. In Eq. [33] ΔH 2nd is the enthalpy of activation for the second sphere water exchange process and k ex 2nd,298 is the corresponding exchange rate at 298 K.

5 k k ex kt B ΔS ΔH kex T ΔH 1 1 = = exp = exp τ m h R RT R T k ΔH T T 2 nd,298 2nd 2nd ex 1 1 ex = exp ll correlation times and the diffusion constant are supposed to obey an rrhenius law: 298 E 1 1 exp a τ = τ R T EGdH 1 1 DGdH = DGdH exp R T [32] [33] [34] [35]

6 Table S1. Proton relaxivities (r 1 / mm -1 s -1 ) of Gd 2 L 1 in the absence of Ca 2+, c(gd 3+ )=5.1 mm, ph=6.25, at 25 and 37 C. ν ( 1 H)/MHz 15.5 C 25 C 37 C

7 Table S2. Proton relaxivities (r 1 / mm -1 s -1 ) of Gd 2 L 1 in the presence of Ca 2+, c(gd 3+ )=3.2 mm, c(ca 2+ )=4.4 mm, ph=7, at 15.5, 25 and 37 C. ν ( 1 H)/MHz 15.5 C 25 C

8 Table S3. Variable temperature reduced transverse and longitudinal 17 O relaxation rates of Gd 2 L 1 in the absence of Ca 2+, c(gd 3+ )=51.8 mm, ph=7, P m = at T. Reference was acidified H 2 O, ph=3.4. t / C T / K 1000/T / K -1 P m T 1 (Gd)/s T 1 (ref)/s T 2 (Gd)/s T 2 (ref)/s ln(1/t 1r ) ln(1/t 2r ) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Table S4. Variable temperature reduced transverse and longitudinal 17 O relaxation rates of Gd 2 L 1 in the presence of 1M Ca 2+, c(gd 3+ )=45.6 mm, ph=7, P m = at T. Reference was acidified 1M CaCl 2. t / C T / K 1000/T / K -1 P m T 1 (Gd)/s T 1 (ref)/s T 2 (Gd)/s T 2 (ref)/s ln(1/t 1r ) ln(1/t 2r ) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

9 Table S5. Relaxometric Ca 2+ titration of Gd 2 L 1 at 25 C, ph 7 and T. c(gd 3+ ) / mm c(ca 2+ ) / mm c(complex) / mm n(ca 2+ ):n(complex) T 1 / ms r 1 / mmol -1 s Table S6. Relaxometric Ca 2+ titration of Gd 2 L 2 at 25 C, ph 7 and T. c(gd 3+ ) / mm c(ca 2+ ) / mm c(complex) / mm n(ca 2+ ):n(complex) T 1 / r 1 / mmol -1 s -1 ms

10 Table S7. Relaxometric Mg 2+ titration of Gd 2 L 1 at 25 C, ph 7 and T. c(gd 3+ ) / mm c(mg 2+ ) / mm c(ca 2+ ) / mm c(complex) / mm n(mg 2+ ):n(complex) n(ca 2+ ):n(complex) r 1 / mmol -1 s

11 Table S8. Luminescence lifetimes measurements on Eu 2 L 1 at 25 C, ph neutral, and the calculated hydration numbers q. n(ca 2+ ):n(complex) τ H2O / ms τ D2O / ms q

12 Figure S1. Variable Ca 2+ concentration UV-Vis studies on Eu 2 L 1 at 50 C. 1,4 equiv. Ca(II) 0,15 0,13 0,11 0,09 0,07 0 equiv. Ca(II) 0,84 0,82 0,8 0,78 0,05 0,03 0,01-0,01-0,03-0,05 10 equiv. Ca(II) 0,76 0,74 0,72 0,7 50 equiv. Ca(II) 0,12 0,1 0,08 0,06 0,04 0,0005 0,0004 0,0003 0,0002 0, ,02-0, ,0002 Figure S2. Variable Ca 2+ concentration UV-Vis studies on Eu 2 L 1 at 37 C. 0 equiv. Ca(II) 1,4 equiv. Ca(II) 0,15 0,84 0,13 0,11 0,09 0,82 0,8 0,07 0,05 0,03 0,01-0,01-0,03-0,05 0,78 0,76 0,74 0,72 0,7 10 equiv. Ca(II) 50 equiv. Ca(II) 0,2 0,19 0,18 0,17 0,0012 0,001 0,0008 0,16 0,15 0,14 0,13 0,12 0,11 0,1 0,0006 0,0004 0, ,0002

13 Figure S3. Variable Ca 2+ concentration UV-Vis studies on Eu 2 L 1 at 25 C. 0 equiv. Ca(II) 1,4 equiv. Ca(II) 0,2 0,1 0,1 0,1 0,1 0,1 0,0 0,0 0,0 0,0 0,15 0,13 0,11 0,09 0,07 0,05 0,03 0,01-0,01-0,03-0,05 10 equiv. Ca(II) 50 equiv. Ca(II) 0,18 0, ,16 0,0002 0, ,14 0,0001 0,12 0, ,1 0-0, ,08-0,0001 0,06-0,00015 Figure S4. Variable Ca 2+ concentration UV-Vis studies on Eu 2 L 1 at 15.5 C. 1,4 equiv.ca(ii) 10 equiv. Ca(II) 0,34 0,02 0,32 0 0,3-0,02 0,28 0,26-0,04 0,24-0,06 0,22-0,08 0,2-0,1

14 Table S9. Fitted parameters of Gd 2 L 1 in the absence of Ca 2+. The underlined parameters were fixed during the fitting. Parameter Gd 2 L 1 k 298 ex [10 6 s -1 ] 2.4±0.2 ΔH [kj mol -1 ] 43.6±3.3 ΔS [J mol -1 K -1 ] /ħ [10 6 rad s -1 ] -3.8 τ 298 RO [ps] 349±47 Ε R [kj mol -1 ] 24±1 τ 298 V [ps] 20.6±2.7 Ε V [kj mol -1 ] 1 Δ 2 [10 20 s -2 ] 0.46±0.10 D 298 GdH [10-10 m 2 s -1 ] 25±3 Ε DGdH [kj mol -1 ] 30±2 δg 2 L [10-1 ] 2.7±0.7 τ RH / τ RO 0.76±0.12 r GdO [Å] 2.5 r GdH [Å] 3.1 r GdHouter [Å] 3.6 χ(1+η 2 /3) 1/2 [MHz] 7.58 q 0.4 q 2nd τ M 2nd [ps] 50 ΔH 298 2nd [kj mol -1 ] 35 r 2nd GdH [Å] 3.5 r 2nd GdO [Å] 4.1

15 Table S10. Fitted parameters of Gd 2 L 1 in the presence of 1M Ca 2+. The underlined parameters were fixed during the fitting. Parameter Gd 2 L 1 + Ca 2+ k 298 ex [10 6 s -1 ] 7.5±1.6 ΔH [kj mol -1 ] 43.6 ΔS [J mol -1 K -1 ] /ħ [10 6 rad s -1 ] -3.8 τ 298 RO [ps] 1152±243 Ε R [kj mol -1 ] 21±6 τ 298 V [ps] 0.13±0.02 Ε V [kj mol -1 ] 1 Δ 2 [10 20 s -2 ] 0.50±0.05 δg 2 L [10-2 ] 2.1 r GdO [Å] 2.5 r GdH [Å] 3.1 r GdHouter [Å] 3.5 χ(1+η 2 /3) 1/2 [MHz] 7.58 q 0.7 q 2nd τ M 2nd [ps] 50 ΔH 298 2nd [kj mol -1 ] 35 r 2nd GdH [Å] 3.5 r 2nd GdO [Å] 4.1

16 Figure S5. IR spectrum of the ligand L 1.

17 Figure S6. IR spectrum of Gd 2 L 1 complex.

18 Figure S7. 1 H NMR spectrum of the compound 6a.

19 Figure S8. 13 C NMR spectrum of the compound 6a.

20 Figure S9. 1 H NMR spectrum of the ligand L 1.

21 Figure S C NMR spectrum of the ligand L 1.

22 Figure S11. 1 H NMR spectrum of the ligand L 2.

23 Figure S C NMR spectrum of the ligand L 2.

24 Figure S13. 1 H- 1 H COSY spectrum of the compound 6a.

25 Figure S14. 1 H- 13 C HSQC spectrum of the compound 6a. References 1 T. J. Swift, R. E. Connick, J. Chem. Phys., 1962, 37, J. R. Zimmermann, W. E. Brittin, J. Phys. Chem., 1957, 61, Z. Luz, S. Meiboom, J. Chem. Phys., 1964, 40, J. H. Freed, J. Chem. Phys., 1978, 68, S. H. Koenig, R. D. Brown III, Prog. Nucl. Magn. Reson. Spectrosc., 1991, 22, 487.